DISCLAIMER: I work in a production facility where we do this all the time your own results may vary so be careful. Plastics(lexan and acrylic) can be fixed with wet sanding. Start off with a low grit sandpaper around 1000 grit and wet it and the surface. We use rubbing alchohol. Clean it up look at it and determine whether or not to go up a notch. You will prolly end up using 1500 grit as the final sandpaper. Best bet is to try this method and any other you hear about on a small section of lexan that you may have lying around.
As far as cleaning it goes glas cleaner an a soft sloth shoud be fine.

After wet sanding (which has worked for me very well), you can use a scratch fixer also. Sanding may leave a slightly dull or rough finish that may not match with the rest of the Lexan. I don’t know the difference between Lexan and acrylic, but Novus makes a scratch remover that works well for acrylic.

I havent had to do this myself yet, but at the hardware store, right next to the plexi and lexan, they sell a polish and scratch remover specifically made for plastics. I dont know how well they work, but if you dont want to try the sandpaper method, then you might want to try something like this.

well, i have plenty of spare lexan lying around (i ruined 3 pieces of lexan while i was building my stick) so i’ll try out a little bit of everything and i’ll be sure to report back here with my results